A catalog of Cayley-Dickson-like products
Rings and Algebras
2015-06-19 v5
Abstract
A catalog of all 32 Cayley-Dickson-like doubling products on ordered pairs (a,b),(c,d) for which (1,0) is the left and right identity and for which xx* and x*x equal the square of the norm of x given the conjugate (a,b)*=(a*,-b). Only eight of these are true Cayley-Dickson doubling products, since 24 of them do not satisfy the quaternion properties. Each of the eight Cayley-Dickson products has a distinctive representation in the Fano Plane.
Keywords
Cite
@article{arxiv.1107.1301,
title = {A catalog of Cayley-Dickson-like products},
author = {John W. Bales},
journal= {arXiv preprint arXiv:1107.1301},
year = {2015}
}